An overview on real division algebras

In this paper, we expose initial concepts of real division algebras, providing historical notes on $\R$, $\C$, $\Ham$ and $\Oct$. This is done to emphasize the relevance of topological K-theory through the Bott-Milnor-Kervaire Theorem, which is at the end. For completeness, we also present two classical results about the main division algebras.